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Terrence writes down one of the numbers from 020 on one index card ea
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27 Jul 2017, 01:21
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49% (03:07) correct 51% (03:25) wrong based on 88 sessions
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Terrence writes down one of the numbers from 020, inclusive, on one index card each until he has written each number exactly once and then faces all the cards down. Next, he randomly chooses two cards without turning them over. What is the probability that a prime number will be written on each card and that the absolute difference between the two prime numbers will itself be a prime number? (A) 1/35 (B) 4/95 (C) 4/105 (D) 8/95 (E) 8/105
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Terrence writes down one of the numbers from 020 on one index card ea
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27 Jul 2017, 03:53
The total ways of picking up 2 numbers from 21 numbers are \(21c2 = \frac{21*20}{2}= 210\) Since we have been asked to find out the probability of finding 2 prime numbers whose difference is a prime number, there are 8 such possibilities For the number pairs {(2,5),(3,5),(2,7),(5,7),(2,13),(11,13),(2,19),(17,19)} The probability that a prime number will be written on each card and that the absolute difference between the two prime numbers will also be a prime number is \(\frac{8}{210}\) = \(\frac{4}{105}\) (Option C)
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Re: Terrence writes down one of the numbers from 020 on one index card ea
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27 Jul 2017, 05:01
Ans :C 21C2=210 And possibilities are 8 (3,5)(5,2)(5,7)(7,2)(11,13)(13,2)(17,19)(19,2) 8/210=4/105 Sent from my Mi 4i using GMAT Club Forum mobile app



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Re: Terrence writes down one of the numbers from 020 on one index card ea
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27 Jul 2017, 05:36
Bunuel wrote: Terrence writes down one of the numbers from 020, inclusive, on one index card each until he has written each number exactly once and then faces all the cards down. Next, he randomly chooses two cards without turning them over. What is the probability that a prime number will be written on each card and that the absolute difference between the two prime numbers will itself be a prime number?
(A) 1/35
(B) 4/95
(C) 4/105
(D) 8/95
(E) 8/105 Total number of cards are 21 21C2 Card choice Denominator will be (21*20)/2 = 210 Option D and B are out Prime number 2, 3, 5, 7, 11, 13, 17, 19 Difference of prime numbers be prime (Favorable selection) = (2,5) (2,7), (2,13), (2,19), (3,5), (5,7), (11,13), (17, 19) and also their reversed order i.e. (5,2) (7,2)..... (8*2)/210 8/105 Option E
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Re: Terrence writes down one of the numbers from 020 on one index card ea
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27 Jul 2017, 05:50
Bunuel wrote: Terrence writes down one of the numbers from 020, inclusive, on one index card each until he has written each number exactly once and then faces all the cards down. Next, he randomly chooses two cards without turning them over. What is the probability that a prime number will be written on each card and that the absolute difference between the two prime numbers will itself be a prime number?
(A) 1/35
(B) 4/95
(C) 4/105
(D) 8/95
(E) 8/105 Prime numbers from 0 to 20 = 2, 3, 5, 7, 11, 13, 17, 19 = 8 values. Let \(a\) be the first card and \(b\) be the second card chosen. Probability that each card has a prime number written on its face = \(\frac{8}{21} * \frac{7}{20} = \frac{2}{3} * \frac{1}{5} = \frac{2}{15}\). Let \((a,b)\) be a pair such that \(ab\) is a prime number, such pairs are \((2,5), (2,7), (2,13), (2,19), (3,5), (5,7), (11,13), (17,19)\). No. of ways 2 cards can be chosen from 8 = \(8c2 = 28\). Probability that \(ab\) is a prime number = \(8/28 = 2/7\). Required probability = \(\frac{2}{15} * \frac{2}{7} = \frac{4}{105}\). Ans  C.
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Re: Terrence writes down one of the numbers from 020 on one index card ea
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27 Jul 2017, 09:11
mynamegoeson wrote: Bunuel wrote: Terrence writes down one of the numbers from 020, inclusive, on one index card each until he has written each number exactly once and then faces all the cards down. Next, he randomly chooses two cards without turning them over. What is the probability that a prime number will be written on each card and that the absolute difference between the two prime numbers will itself be a prime number?
(A) 1/35
(B) 4/95
(C) 4/105
(D) 8/95
(E) 8/105 Total number of cards are 21 21C2 Card choice Denominator will be (21*20)/2 = 210 Option D and B are out Prime number 2, 3, 5, 7, 11, 13, 17, 19 Difference of prime numbers be prime (Favorable selection) = (2,5) (2,7), (2,13), (2,19), (3,5), (5,7), (11,13), (17, 19) and also their reversed order i.e. (5,2) (7,2)..... (8*2)/210 8/105 Option E Hi mynamegoeson, Since absolute difference between primes is required, does it matter whether the guy picks up in the sequence of 1113 or 1311?



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Re: Terrence writes down one of the numbers from 020 on one index card ea
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28 Jul 2017, 04:19
Dkingdom wrote: mynamegoeson wrote: Bunuel wrote: Terrence writes down one of the numbers from 020, inclusive, on one index card each until he has written each number exactly once and then faces all the cards down. Next, he randomly chooses two cards without turning them over. What is the probability that a prime number will be written on each card and that the absolute difference between the two prime numbers will itself be a prime number?
(A) 1/35
(B) 4/95
(C) 4/105
(D) 8/95
(E) 8/105 Total number of cards are 21 21C2 Card choice Denominator will be (21*20)/2 = 210 Option D and B are out Prime number 2, 3, 5, 7, 11, 13, 17, 19 Difference of prime numbers be prime (Favorable selection) = (2,5) (2,7), (2,13), (2,19), (3,5), (5,7), (11,13), (17, 19) and also their reversed order i.e. (5,2) (7,2)..... (8*2)/210 8/105 Option E Hi mynamegoeson, Since absolute difference between primes is required, does it matter whether the guy picks up in the sequence of 1113 or 1311? Yes i think it should be 4/105 since difference is required
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Re: Terrence writes down one of the numbers from 020 on one index card ea
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